The free energy density in Eq. (REF ) is equivalent to the earlier form of the GL model used in a general hydrodynamic formulation and in studies of some topological properties of the SC mixtures [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}; in these works the quantum pressure and the gradient-coupling are implicit.
The equations for wave functions with either only momentum-coupling, or only gradient-coupling were studied in [11]}, [12]}, [13]}.
